Dynamical quantum phase transition, metastable state, and dimensionality reduction: Krylov analysis of fully connected spin models
arXiv:2504.07474 · doi:10.1103/m4jf-7svp
Abstract
We study quenched dynamics of fully-connected spin models. The system is prepared in a ground state of the initial Hamiltonian and the Hamiltonian is suddenly changed to a different form. We apply the Krylov subspace method to map the system onto an effective tridiagonal Hamiltonian. The state is confined in a potential well and is time-evolved by nonuniform hoppings. The dynamical singularities for the survival probability can occur when the state is reflected from a potential barrier. Although we do not observe any singularity in the spread complexity, we find that the entropy exhibits small dips at the singular times. We find that the presence of metastable state affects long-time behavior of the spread complexity, and physical observables. We also observe a reduction of the state-space dimension when the Hamiltonian reduces to a classical form.
arXiv comment11 pages, 17 figures, minor changes for v2
References in corpus (24)
- Nonequilibrium dynamics of closed interacting quantum systems
- Quantum many-body systems out of equilibrium
- Time-dependence of correlation functions following a quantum quench
- Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
- Dynamical quantum phase transitions: a review
- Direct observation of dynamical quantum phase transitions in an interacting many-body system
- A Universal Operator Growth Hypothesis
- Quantum chaos and the complexity of spread of states
- Dynamical quantum phase transitions: scaling and universality
- Quantum quench dynamics
- Dynamical quantum phase transitions in systems with broken-symmetry phases
- Operator complexity: a journey to the edge of Krylov space
- On The Evolution Of Operator Complexity Beyond Scrambling
- Excited-state quantum phase transitions
- Quantum Dynamics in Krylov Space: Methods and Applications
- Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
- Universal relation for operator complexity
- Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model
- Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
- Complex semiclassical analysis of the Loschmidt amplitude and dynamical quantum phase transitions
- Complexity in the Lipkin-Meshkov-Glick Model
- Krylov complexity for non-local spin chains
- Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
- Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators